Answer
Assuming only one chromosomal crossover was possible and the genes on either side of the chromosome were both dominant, then only half of the children would receive one trait or another. The children would not carry both the genes like the parent, as compared to actuality. In actuality, because there are multiple gene crossovers the resulting children can inherit both genes instead of one or the other.
Work Step by Step
During the metaphase the mieotic spindle takes the chromatids from one homolog and attaches them at random to the chromatids of the other homolog. This is done multiple times, resulting in the offspring carrying both of the dominant genes that are being carried on the opposite ends of the parent homolog. However, if this crossover was only done once, the resulting chromosomes will only have either the gene that was on one end of the parent homolog or the gene that was on the other end of the parent homolog, as it only had one chance to go through the mieotic spindle.
